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    Question

    You are given with a question followed by 2 statements.

    Identify that which statement(s) is/are necessary/ sufficient to answer the question? 3x + y = 23. Find the value of ‘y’. Statement  I: x2 – 10x + 25 = 0 Statement  II: 2x + 2y = 26 
    A Statement I alone is sufficient. Correct Answer Incorrect Answer
    B Statement II alone is sufficient. Correct Answer Incorrect Answer
    C Either statement I or statement II alone is sufficient. Correct Answer Incorrect Answer
    D Statements I and II together are necessary. Correct Answer Incorrect Answer

    Solution

    From statement I: x2 – 5x – 5x + 25 = 0 Or, x(x – 5) – 5(x – 5) = 0 Or, (x – 5)(x – 5) = 0 Or, x = 5 Substituting this value in the question, 3x + y = 15 + y = 23 Or, y = 23 – 15 = 8 So, statement I alone is sufficient. From statement II: x + y = 26/2 = 13 So, 3x + 3y = 13 × 3 = 39 3x + 3y – (3x + y) = 39 – 23 Or, 2y = 16 Or, y = (16/2) = 8 So, statement II alone is sufficient. Therefore, either statement I or statement II alone is sufficient.

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